5.95 In checking river water samples for bacteria, water is placed in a culture medium so that certain bacteria colonies can grow if those bacteria are present. The number of colonies per dish averages 12 for water samples from a certain river.

a Find the probability that the next dish observed will have at least 10 colonies.

b Find the mean and standard deviation of the number of colonies per dish.

c Without calculating exact Poisson probabilities, find an interval in which at least 75% of the colony count measurements should lie.